New perspective on thermodynamics of spacetime: The emergence of unimodular gravity and the equivalence of entropies

TL;DR

This paper derives Einstein equations from thermodynamic principles, showing the equivalence of entanglement and Clausius entropies, and reveals that spacetime thermodynamics naturally leads to unimodular gravity instead of general relativity.

Contribution

It provides a novel derivation of Einstein equations from entropy balance and establishes the equivalence of different entropies, highlighting unimodular gravity as the underlying gravitational theory.

Findings

Einstein equations derived from Clausius and entanglement entropy balance.

Equivalence of matter entanglement and Clausius entropy in semiclassical regime.

Gravitational dynamics from thermodynamics corresponds to unimodular gravity.

Abstract

We present a novel derivation of Einstein equations from the balance between Clausius entropy crossing the boundary of a local causal diamond and entanglement entropy associated with its horizon. Comparing this derivation with the entanglement equilibrium approach developed by Jacobson, we are able to argue for the equivalence of matter entanglement and Clausius entropy in the semiclassical regime. We also provide a direct comparison of both entropies for conformal matter, showing their equivalence without appealing to gravitational dynamics. Furthermore, we determine that gravitational dynamics implied by thermodynamics of spacetime, in fact, corresponds to unimodular gravity rather than general relativity.